Downward migration credit risk problem: a non-homogeneous backward semi-Markov reliability approach
针对马尔可夫模型在信用评级迁移中拟合不佳的问题，提出一种非齐次向后半马尔可夫模型，考虑状态转移的非齐次性、向下迁移问题和时间随机性，并基于标准普尔历史数据进行实证分析。
International organizations evaluate credit risk and rank firms according to risk by assigning them a ‘rating’. The time evolution of a rating can be studied by means of Markov models. Some papers have outlined the problem pertaining to the unsuitable fitting of Markov processes in a credit risk environment. This paper presents a model that overcomes the problems given by the Markov rating models. It includes non-homogeneity, the downward problem and the randomness of time in the transitions of states, thus making it possible to consider the duration inside a state in a complete way. In this paper, both, the transient and asymptotic analyses are presented. The asymptotic analysis is performed by using a mono-unireducible topological structure. Moreover, a real data application is conducted using the historical database of Standard & Poor’s as the source.